Works such as the ads created by the graphic designer you hired, are protected under the Copyright Act from the time htey are created, written down or otherwise set into tangible form, no registration necessary.
Normally, the copyrights in the work (right to copy, distribute, display, perform, make derivative works through modification, etc) immediately becomes the property of the author who created the work. In the case of an employee of a business whose job is to create the work, the business is considered the author. Here, however, you describe a situation where you hired an independent contractor to create the ads, rather than assign the task to one of your employees.
When a business hires an independent contractor to create the work, the contractor -- not the business -- is the author unless (A) the work is of a type which can be characterized as a "work made for hire" under the Copyright Act (yours falls into that category); AND (B) the contractor signs a written agreement that the work will be a work made for hire.
You don't say whether you signed any kind of agreement stating that the ads would be treated as a work for hire, nor do you suggest any prior course of dealing under which you might have already been operating under such an agreement.
However, the fact that you are even asking the question is ample evidence that you did not have such an agreement in place. For that reason, I would tell you that the graphic designer, and not you, owns the ads.
I concur with my colleague.
Absent any written work-for-hire / assignment agreement, the designer will be the "owner" of the ad but you get an implied license to use the ad for its intended purposes and this right cannot be frustrated by the designer (e.g., by them selling your competitor the same or similar ad).
What this means practically speaking is that you get to use the work done as intended but you could not, for example, sell the design to Bono for U2's new album cover. The designer however would be able to do this because the IP still belongs to her and this transaction does not frustrate or diminish the value of the work you paid for.
Of course, all of this assumes that the ad we are talking about warrants copyright protection.
The broader context to your narrative is missing here. You may wish to discuss with a lawyer in private. Most of us here, including myself, offer a free phone consult.
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More details are necessary to answer your question. Is the graphic designer an employee of the newspaper, your company or an independent contractor? Was there a written agreement between the parties?
As stated before, if you paid someone to design an advertisement for you, and there is no written contract, you are granted an implied license to use the advertisement. The graphic designer cannot comeback and demand more money for your continued use of the advertisement.
Consult with an attorney in your area to confirm.
Unless the graphic designer was an employee or you had a lawyer prepare a copyright assignment (oops, right?), the designer owns them. See an IP attorney and get this solved both for this and for the future.Consider this a lesson and learn from it how pros do this stuff.
I am not your lawyer and you are not my client. Free advice here is without recourse and any reliance thereupon is at your sole risk. This is done without compensation as a free public service. I am licensed in IL, MO, TX and I am a Reg. Pat. Atty. so advice in any other jurisdiction is strictly general advice and should be confirmed with an attorney licensed in that jurisdiction.